A Bound Quantum Particle in a Riemann-Cartan space with Topological Defects and Planar Potential

TL;DR

This paper investigates the quantum behavior of a spin-1/2 particle in a Riemann-Cartan space with topological defects, magnetic fields, and potentials, deriving exact energy solutions and comparing with the Aharonov-Bohm effect.

Contribution

It provides exact solutions for a bound quantum particle in a defected Riemann-Cartan space considering spin-torsion and magnetic interactions, extending previous models.

Findings

Exact energy eigenfunctions and eigenvalues derived.

Analysis of the singular defect limit and comparison with Aharonov-Bohm effect.

Insights into spin-torsion and magnetic field interactions in quantum systems.

Abstract

Starting from a continuum theory of defects, that is the analogous to three-dimensional Einstein-Cartan-Sciama-Kibble gravity, we consider a charged particle with spin 1/2 propagating in a uniform magnetic field coincident with a wedge dispiration of finite extent. We assume the particle is bound in the vicinity of the dispiration by long range attractive (harmonic) and short range (inverse square) repulsive potentials. Moreover, we consider the effects of spin-torsion and spin-magnetic field interactions. Exact expressions for the energy eigenfunctions and eigenvalues are determined. The limit, in which the defect region becomes singular, is considered and comparison with the electromagnetic Aharonov-Bohm effect is made.